424 
PHYSICS: BRINSMADE AND KEMBLE 
of the two components. We therefore look upon the small wave length 
discrepancy referred to as an indication of a slight error in the accepted 
values of the infra-red refractive indices of quartz. 
The Asymmetry oj the Bands. — According to the elementary theory 
of the structure of the infra-red absorption bands of diatomic gases 
given by Bjerrum^, the curve obtained when absorption coefficients are 
plotted against frequency should be a symmetric doublet, of which each 
half should have the form of the distribution function for angular 
velocities. He assumes implicitly that the frequency of the atomic 
vibration is independent of the angular velocity of the molecule. The 
observed absorption bands are all asymmetric, however, the high fre- 
quency component being narrower and more intense. In an unpub- 
lished paper read before a recent meeting of the American Physical 
Society by Kemble^, it was suggested that this asymmetry might be 
due to the fact that the frequency of the atomic vibration is lowered by 
the expansion of the molecule under the influence of the centrifugal force 
produced by the molecular rotation. This change of frequency would 
cause a crowding together of the quantum lines in the high frequency 
component and a corresponding increased separation in the low fre- 
quency component. On the basis of this theory the frequency of 
vibration should be 
where is a constant, vq is the frequency of vibration for zero angular 
velocity, and vr is the frequency of rotation. Combining this assump- 
tion with the quantum theory we obtain the following formula for the 
positions of the two elementary lines corresponding to the ^th unit of 
angular velocity. 
V = vq ^ pvi —ap^vi. 
vi is the unit of angular frequency. The dashed vertical lines on figure 
4 indicate the theoretical positions of the quantum lines in the HCl har- 
monic as computed by the above formula, using the values 3.7 X 10"^^ 
and 6.32 X 10^^ for a and vi respectively. The vertical lines in figure 5 
give the corresponding positions for the fundamental, using the values 
2.55 X 10~^^ and 6.32 X lO^^ for a and Pi. In each case the agreement 
is satisfactory. 
The unit of angular frequency, vi, is inversely proportional to the mo- 
ment of inertia of the molecule and v. Bahr interpreted an apparent 
decrease in the value of vi, for the larger values of p which was observable 
on her absorption curve for the HCl fundamental, as an indication of an 
increase in the moment of inertia with increasing angular velocity. 
It will be observed that our observations show no perceptible variation 
in the value of i^i. 
